arXiv subjects

Honglin Luo

Publications and source records attributed to Honglin Luo.

3 recordsLinked to original sources

arXiv2026

Modulus of conically averaged mappings and its applications to angles between two subspaces

Conically averaged mappings, a generalization of averaged mappings, are important in a wide range of Optimization Algorithms. In this paper, we propose the modulus of conical averagedness to classify conical averaged mappings. Introducing the monotone and comonotone values of generalized monotone mappings, we investigate their connections to the modulus of conical averagedness. In the linear setting, we completely characterize conically averaged matrices, and derive explicit and pleasing formulae for computing their modulus of averagedness. As applications, we compute the Dixmier and Friedrichs angles between two subspaces. Nonlinear results are established as extensions of the linear case. Conical averagedness of proximal and reflection mappings of hypoconvex functions are also studied.

math.OC↗

arXiv2026

On Characterizations of (Almost) Strictly Convex Functions

In this paper, we unify and improve existing results on characterizing strict and almost stricty convex functions via subdifferential mapping, Moreau envelope, and proximal mappings. In particular, it is shown that if a convex function is subdifferentiable on its domain, then it is strictly convex if and only if its subdifferential is strictly monotone, equivalently, almost strictly monotone. Rockafellar-Wets' characterizations of almost strictly convex functions via almost differentiability of Fenchel conjugates and strict monotonicity of subdifferentials are extended from a finite-dimensional space to a Hilbert space. We also establish similar results for paramonotone operators.

math.CA↗

arXiv2024

Level proximal subdifferential, variational convexity, and pointwise quadratic approximation

Level proximal subdifferential was introduced by Rockafellar recently for studying proximal mappings of possibly nonconvex functions. In this paper a systematic study of level proximal subdifferential is given. We characterize variational convexity of a function by local firm nonexpansiveness of proximal mappings or local relative monotonicity of level proximal subdifferential, and use them to study local convergence of proximal gradient method and others for variationally convex functions. Variational sufficiency guarantees that proximal gradient method converges to local minimizers rather than just critical points. We also investigate the existence, single-valuedness and integration of level proximal subdifferential, and quantify pointwise quadratic approximation (or Lipschitz smoothness) of a function. As a powerful tool, level proximal subdifferential provides deep insights into variational analysis and optimization.

math.OC↗